F-blowups and essential divisors for toric varieties
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916212976386048 |
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| author | Chávez-Martínez, Enrique Duarte, Daniel Yasuda, Takehiko |
| author_facet | Chávez-Martínez, Enrique Duarte, Daniel Yasuda, Takehiko |
| contents | We investigate the relation between essential divisors and F-blowups, in particular, address the problem whether all essential divisors appear on the $e$-th F-blowup for large enough $e$. Focusing on the case of normal affine toric varieties, we establish a simple sufficient condition for a divisor over the given toric variety to appear on the normalized limit F-blowup as a prime divisor. As a corollary, we show that if a normal toric variety has a crepant resolution, then the above problem has a positive answer, provided that we use the notion of essential divisors in the sense of Bouvier and Gonzalez-Sprinberg. We also provide an example of toric threefold singularities for which a non-essential divisor appears on an F-blowup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_13247 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | F-blowups and essential divisors for toric varieties Chávez-Martínez, Enrique Duarte, Daniel Yasuda, Takehiko Algebraic Geometry 14E15, 14M25, 14B10 We investigate the relation between essential divisors and F-blowups, in particular, address the problem whether all essential divisors appear on the $e$-th F-blowup for large enough $e$. Focusing on the case of normal affine toric varieties, we establish a simple sufficient condition for a divisor over the given toric variety to appear on the normalized limit F-blowup as a prime divisor. As a corollary, we show that if a normal toric variety has a crepant resolution, then the above problem has a positive answer, provided that we use the notion of essential divisors in the sense of Bouvier and Gonzalez-Sprinberg. We also provide an example of toric threefold singularities for which a non-essential divisor appears on an F-blowup. |
| title | F-blowups and essential divisors for toric varieties |
| topic | Algebraic Geometry 14E15, 14M25, 14B10 |
| url | https://arxiv.org/abs/2304.13247 |